A. यह सांत है क्योंकि हर का अभाज्य गुणनखंड केवल (2) और (5) हैं/It is terminating because the denominator has only (2) and (5) as prime factors
Step 1
Concept
\(40=2^3\times5\), so the decimal will terminate. In exams, check the prime factors of the denominator.
Step 2
Why this answer is correct
The correct answer is A. यह सांत है क्योंकि हर का अभाज्य गुणनखंड केवल (2) और (5) हैं / It is terminating because the denominator has only (2) and (5) as prime factors. \(40=2^3\times5\), so the decimal will terminate. In exams, check the prime factors of the denominator.
Step 3
Exam Tip
\(40=2^3\times5\), इसलिए दशमलव सांत होगा। परीक्षा में हर के अभाज्य गुणनखंड जाँचें।
The denominator contains (3), which is not (2) or (5). Therefore the decimal is non-terminating recurring.
Step 2
Why this answer is correct
The correct answer is B. असांत आवर्ती / Non-terminating recurring. The denominator contains (3), which is not (2) or (5). Therefore the decimal is non-terminating recurring.
Step 3
Exam Tip
हर में (3) है, जो (2) या (5) नहीं है। इसलिए दशमलव असांत आवर्ती होगा।
\(\sqrt{2}\times\sqrt{8}=\sqrt{16}=4\), which is rational. The product of two irrational numbers is not always irrational.
Step 2
Why this answer is correct
The correct answer is B. परिमेय संख्या / Rational number. \(\sqrt{2}\times\sqrt{8}=\sqrt{16}=4\), which is rational. The product of two irrational numbers is not always irrational.
Step 3
Exam Tip
\(\sqrt{2}\times\sqrt{8}=\sqrt{16}=4\), जो परिमेय है। दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता।
C. यह असांत अनावर्ती दशमलव है/It is a non-terminating non-recurring decimal
Step 1
Concept
\(\sqrt{3}\) is irrational, so its decimal is non-terminating non-recurring. Identify perfect squares in square roots.
Step 2
Why this answer is correct
The correct answer is C. यह असांत अनावर्ती दशमलव है / It is a non-terminating non-recurring decimal. \(\sqrt{3}\) is irrational, so its decimal is non-terminating non-recurring. Identify perfect squares in square roots.
Step 3
Exam Tip
\(\sqrt{3}\) अपरिमेय है, इसलिए इसका दशमलव असांत अनावर्ती होता है। वर्गमूल में पूर्ण वर्ग पहचानें।
The denominator (7) is neither (2) nor (5), so the decimal is non-terminating recurring. It is still rational.
Step 2
Why this answer is correct
The correct answer is B. असांत आवर्ती / Non-terminating recurring. The denominator (7) is neither (2) nor (5), so the decimal is non-terminating recurring. It is still rational.
Step 3
Exam Tip
(7) हर में (2) या (5) नहीं है, इसलिए दशमलव असांत आवर्ती होगा। यह फिर भी परिमेय संख्या है।
